“…Complete/partial cheap control problems appear in many topics of optimal control, H ∞ control and differential games theories. For example, such problems appear in the following topics: (1) solution of singular optimal control problems by regularization (see, e.g., [5,9,10,11,12,13]); (2) solution of singular H ∞ control problems by regularization (see, e.g., [14,15,16]); (3) solution of singular differential games by regularization (see, e.g., [17,18,19,20,21,37]); (4) limitation analysis for optimal regulators and filters (see, e.g., [7,13,22,32,36,38]); (5) extremal control problems with high gain control in dynamics (see, e.g., [30,44]); (6) inverse optimal control problems (see, e.g., [34]); (7) robust optimal control of systems with uncertainties/disturbances (see, e.g., [39,40]); (8) guidance/interception problems (see, e.g., [38,41,42]).…”